Question

In: Statistics and Probability

Weekly demand for golf balls at the Happy Valley Golf Club pro shop is normally distributed...

  1. Weekly demand for golf balls at the Happy Valley Golf Club pro shop is normally distributed with a mean of 23 cases and a standard deviation of 6.5 cases. The club gets a profit of $24 per case.
  1. Simulate 52 weeks of demand, and calculate the average weekly profit.

  1. What is the probability that weekly profit will exceed $500?

Solutions

Expert Solution

For the part (a) we have to simulate 52 sample from N( 23 , 6.52 ). Then take the average of 52 samples. This average will give us the average weekly profit.

R code with outputs :

x=rnorm(52,mean=23,sd=6.5) ## simulating random sample

##... the generated random sample


  20.704169 25.221456 29.272282 14.346871 24.036673 24.340370 20.598006
33.971030 21.741900 41.558686 20.029663 23.666392 20.439161 24.185303
30.651066 16.330701 21.872000 19.914429 17.857747 26.383415 31.898270
18.300568 26.980371 19.337225 23.108444 18.900966 21.952243 29.100218
26.280539 7.181248 20.449257 24.466836 17.086236 16.897833 28.606257
17.616832 24.118150 22.682653 13.329532 22.911879 17.818902 17.638422
23.527078 19.788865 24.629377 25.263527 25.271971 15.779744 22.238125
29.683797 21.513359 24.161373

##..... average

mean(x)

22.60849 ## answer.

Hence the average weekly profit is 22.60849.

Part b


orchestra answered 2 years ago
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